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Statistics · Probability

Expected Value Decision Calculator

Compare two uncertain choices by net expected value, loss probability, outcome range, and the probability needed for a binary option to break even.

Statistics · Probability

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Private in-browser calculation · explicit assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

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Understand the probability

What the expected value decision calculator is calculating

Connecting outcomes, probabilities, and long-run value. A discrete random variable assigns a numerical value to every possible outcome. Its distribution supports expected value and variance, but an expectation is a long-run average—not a guaranteed single outcome.

Probability rule

Net EV=Σpᵢxᵢ−fixed cost; binary break-even success probability=(cost−failure outcome)/(success−failure).

Every probability must remain between 0 and 1, and overlapping regions must be jointly feasible. The calculator rejects combinations that violate the stated model.

How to interpret it

Higher expected value does not automatically dominate when downside, liquidity, risk tolerance, or nonfinancial consequences differ.

Model boundary: Each option’s probabilities must total one; monetary or utility values must use a common scale and fixed costs apply in every outcome.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the expected value decision calculator works

Net EV=Σpᵢxᵢ−fixed cost; binary break-even success probability=(cost−failure outcome)/(success−failure).

Higher expected value does not automatically dominate when downside, liquidity, risk tolerance, or nonfinancial consequences differ.

Worked example

Expected Value Decision example

A 40% chance of 100 and 60% chance of 0 with cost 25 has net expected value 15 and break-even success probability 25%.

Net EV=Σpᵢxᵢ−fixed cost; binary break-even success probability=(cost−failure outcome)/(success−failure).

Supported inputs

Precision and limits

Model and design

Each option’s probabilities must total one; monetary or utility values must use a common scale and fixed costs apply in every outcome.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

Higher expected value does not automatically dominate when downside, liquidity, risk tolerance, or nonfinancial consequences differ.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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